Search and Rescue on the Line

Jared Coleman, Loránd Cheng, Bhaskar Krishnamachari

Abstract:

We propose and study a problem inspired by a common task
in disaster, military, and other emergency scenarios: search and rescue.
Suppose an object (victim, message, target, etc.) is at some unknown
location on a path. Given one or more mobile agents, also at initially
arbitrary locations on the path, the goal is to find and deliver the object
to a predefined destination in as little time as possible. We study the
problem for the one- and two-agent cases and consider scenarios where
the object and agents are arbitrarily (adversarially, even) placed along a
path of either known (and finite) or unknown (and potentially infinite)
length. We also consider scenarios where the destination is either at the
endpoint or in the middle of the path. We provide both deterministic
and randomized online algorithms for each of these scenarios and prove
bounds on their (expected) competitive ratios.